Nuprl Lemma : nwkl!-implies-fan
nWKL! ⇒ Fan
Proof
Definitions occuring in Statement :
nwkl!: nWKL!,
fan: Fan,
implies: P ⇒ Q
Definitions unfolded in proof :
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A
Lemmas referenced :
twkl!-implies-dfan,
bool_wf,
twkl!_wf,
nwkl!-iff-twkl!-bool,
fan-iff-dfan-bool,
nwkl!_wf,
dfan_wf,
false_wf,
le_wf,
equipollent-two,
equipollent_wf,
int_seg_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesis,
independent_functionElimination,
isectElimination,
addLevel,
impliesFunctionality,
productElimination,
functionEquality,
dependent_pairFormation,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
hypothesisEquality,
setElimination,
rename
Latex:
nWKL! {}\mRightarrow{} Fan
Date html generated:
2016_05_14-PM-04_13_01
Last ObjectModification:
2015_12_26-PM-07_53_50
Theory : fan-theorem
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