Nuprl Lemma : decidable__equal_nat
∀x,y:ℕ. Dec(x = y ∈ ℕ)
Proof
Definitions occuring in Statement :
nat: ℕ,
decidable: Dec(P),
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
prop: ℙ,
not: ¬A,
so_lambda: λ2x.t[x],
so_apply: x[s],
false: False
Lemmas referenced :
decidable__int_equal,
subtype_base_sq,
int_subtype_base,
not_wf,
equal_wf,
nat_wf,
set_subtype_base,
le_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
unionElimination,
inlFormation,
instantiate,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
sqequalRule,
inrFormation,
introduction,
lambdaEquality,
natural_numberEquality,
voidElimination,
because_Cache
Latex:
\mforall{}x,y:\mBbbN{}. Dec(x = y)
Date html generated:
2016_05_14-AM-06_06_13
Last ObjectModification:
2015_12_26-AM-11_46_52
Theory : equality!deciders
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