Nuprl Lemma : weak-konig-lemma!
WKL!
Proof
Definitions occuring in Statement :
wkl!: WKL!
Definitions unfolded in proof :
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
dfan: Fan_d(T),
all: ∀x:A. B[x],
dbar: dbar(T;X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
exists: ∃x:A. B[x],
ubar: ubar(T;X),
prop: ℙ,
so_lambda: λ2x.t[x],
nat: ℕ,
int_seg: {i..j-},
subtype_rel: A ⊆r B,
so_apply: x[s],
uimplies: b supposing a,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A
Lemmas referenced :
fan-iff-wkl!,
fan-iff-dfan-bool,
fan-theorem,
all_wf,
nat_wf,
bool_wf,
exists_wf,
int_seg_wf,
map_wf,
subtype_rel_dep_function,
int_seg_subtype_nat,
false_wf,
subtype_rel_self,
upto_wf,
dbar_wf,
list_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
productElimination,
thin,
independent_functionElimination,
lambdaFormation,
isectElimination,
hypothesisEquality,
hypothesis,
dependent_pairFormation,
functionEquality,
sqequalRule,
lambdaEquality,
natural_numberEquality,
setElimination,
rename,
applyEquality,
because_Cache,
independent_isectElimination,
independent_pairFormation,
cumulativity,
universeEquality
Latex:
WKL!
Date html generated:
2016_05_15-PM-10_05_31
Last ObjectModification:
2015_12_27-PM-05_50_45
Theory : bar!induction
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