Nuprl Lemma : nsub2-flip
∀[x,y:ℕ2]. uiff((1 - x) = y ∈ ℕ2;x = (1 - y) ∈ ℕ2)
Proof
Definitions occuring in Statement :
int_seg: {i..j-},
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
subtract: n - m,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
int_seg: {i..j-},
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
subtract: n - m,
uiff: uiff(P;Q),
and: P ∧ Q,
prop: ℙ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
less_than: a < b,
squash: ↓T,
true: True
Lemmas referenced :
equal_wf,
decidable__lt,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermSubtract_wf,
intformle_wf,
intformand_wf,
decidable__le,
subtract_wf,
equal-wf-base-T,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermConstant_wf,
intformeq_wf,
intformnot_wf,
satisfiable-full-omega-tt,
lelt_wf,
int_seg_cases,
false_wf,
int_seg_subtype,
int_seg_wf,
equal-wf-base,
int_seg_properties,
int_subtype_base,
subtype_base_sq,
decidable__equal_int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
hypothesis,
unionElimination,
instantiate,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
because_Cache,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
sqequalRule,
independent_pairFormation,
baseClosed,
hypothesis_subsumption,
addEquality,
lambdaFormation,
applyEquality,
lambdaEquality,
setEquality,
productElimination,
dependent_pairFormation,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
dependent_set_memberEquality,
imageMemberEquality,
independent_pairEquality,
axiomEquality,
int_eqEquality
Latex:
\mforall{}[x,y:\mBbbN{}2]. uiff((1 - x) = y;x = (1 - y))
Date html generated:
2016_06_16-PM-05_35_22
Last ObjectModification:
2016_01_18-PM-04_57_12
Theory : cubical!sets
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