Nuprl Lemma : square-board-subtype
∀[n:ℕ]. ∀[T,S:Type]. square-board(n;T) ⊆r square-board(n;S) supposing T ⊆r S
Proof
Definitions occuring in Statement :
square-board: square-board(n;T),
nat: ℕ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
square-board: square-board(n;T),
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
nat: ℕ,
int_seg: {i..j-},
guard: {T},
ge: i ≥ j ,
lelt: i ≤ j < k,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
so_apply: x[s],
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_rel_sets,
list_wf,
equal_wf,
length_wf,
all_wf,
int_seg_wf,
select_wf,
int_seg_properties,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
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,
decidable__lt,
intformless_wf,
intformeq_wf,
int_formula_prop_less_lemma,
int_formula_prop_eq_lemma,
subtype_rel_set,
subtype_rel_list,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
productEquality,
intEquality,
setElimination,
rename,
because_Cache,
natural_numberEquality,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
lambdaFormation,
axiomEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[T,S:Type]. square-board(n;T) \msubseteq{}r square-board(n;S) supposing T \msubseteq{}r S
Date html generated:
2017_10_01-AM-09_06_29
Last ObjectModification:
2017_07_26-PM-04_46_34
Theory : general
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