Nuprl Lemma : nat-deq_wf
NatDeq ∈ EqDecider(ℕ)
Proof
Definitions occuring in Statement :
nat-deq: NatDeq,
deq: EqDecider(T),
nat: ℕ,
member: t ∈ T
Definitions unfolded in proof :
deq: EqDecider(T),
nat-deq: NatDeq,
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
squash: ↓T,
le: A ≤ B,
prop: ℙ,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
iff_wf,
all_wf,
assert_wf,
assert_of_eq_int,
le_wf,
equal_wf,
nat_wf,
eq_int_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
dependent_set_memberEquality,
lambdaEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaFormation,
independent_pairFormation,
applyEquality,
imageMemberEquality,
baseClosed,
equalityUniverse,
levelHypothesis,
introduction,
productElimination,
natural_numberEquality,
intEquality,
addLevel,
allFunctionality,
impliesFunctionality,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination
Latex:
NatDeq \mmember{} EqDecider(\mBbbN{})
Date html generated:
2016_05_14-AM-06_07_00
Last ObjectModification:
2016_01_14-PM-07_31_53
Theory : equality!deciders
Home
Index