Nuprl Lemma : weak-continuity-bool-bool
weak-continuity(𝔹;𝔹)
Proof
Definitions occuring in Statement :
weak-continuity: weak-continuity(T;V),
bool: 𝔹
Definitions unfolded in proof :
weak-continuity: weak-continuity(T;V),
all: ∀x:A. B[x],
member: t ∈ T,
squash: ↓T,
exists: ∃x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
nat: ℕ,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
true: True,
prop: ℙ,
cand: A c∧ B,
quotient: x,y:A//B[x; y],
int_seg: {i..j-},
lelt: i ≤ j < k,
less_than: a < b,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
strong-continuity2-implies-weak-skolem-cantor,
istype-nat,
bool_wf,
int_seg_wf,
subtype_rel_function,
nat_wf,
int_seg_subtype_nat,
istype-false,
subtype_rel_self,
istype-true,
squash_wf,
equal_wf,
member_wf,
true_wf,
istype-universe,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
istype-le,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
imageElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
functionIsType,
universeIsType,
productIsType,
inhabitedIsType,
because_Cache,
equalityIstype,
isectElimination,
natural_numberEquality,
applyEquality,
lambdaEquality_alt,
setElimination,
rename,
independent_isectElimination,
independent_pairFormation,
promote_hyp,
productEquality,
functionEquality,
pointwiseFunctionality,
pertypeElimination,
productElimination,
independent_functionElimination,
sqequalBase,
equalitySymmetry,
equalityTransitivity,
dependent_pairFormation_alt,
functionExtensionality_alt,
instantiate,
universeEquality,
dependent_set_memberEquality_alt,
unionElimination,
approximateComputation,
int_eqEquality,
Error :memTop,
voidElimination
Latex:
weak-continuity(\mBbbB{};\mBbbB{})
Date html generated:
2020_05_20-AM-07_47_46
Last ObjectModification:
2020_01_24-PM-01_59_43
Theory : basic
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